Q. 14.2( 15 Votes )
How much paper of each shade is needed to make a kite given in Fig. 12.4, in which ABCD is a square with diagonal 44 cm.
AC = BD = 44cm
AO = 44/2 = 22cm
BO = 44/2 = 22cm
AB2 = AO2 + BO2
⇒ AB2 = 222 + 222
⇒ AB2 = 2 × 222
⇒ AB = 22√ 2 cm
Area of square = (Side)2 = (22√2)2 = 968 cm2
Area of each triangle (I, II, III, IV) = Area of square /4 = 968 /4 = 242 cm2
Area of lower triangle,
a = 28, b = 28, c = 14
s = (a + b + c)/2
⇒ s = (28 + 28 + 14)/2 = 70/2 = 35.
Area(Δ) = √s(s-a)(s-b)(s-c)
⇒ Area(Δ) = √35(35-28)(35-28)(35-14)
⇒ Area(Δ) = √35×7×7×21
⇒ Area(Δ) = 49√15 = 189.77cm2
Area of Red = Area of IV = 242 cm2
Area of Yellow = Area of I + Area of II = 242 + 242 = 484 cm2
Area of Green = Area of III + Area of lower triangle = 242 + 189.77 = 431.77 cm2
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